WAEC 2023 · Paper 2 · Q14

(a)
A particle is projected at an angle of $42^\circ$ with a velocity of $68\text{ m s}^{-1}$ . Calculate, correct to one decimal place, the: (i) greatest height travelled; (ii) time of flight; (iii) horizontal range travelled. $[g = 10\text{ m s}^{-2}]$ Enter the three values.
Separate values with commas, e.g. 3, −2
(b)
A non-uniform beam $PQ$ of length $15\text{ m}$ and weight $120\text{ N}$ rests horizontally on supports at $P$ and $Q$ . If the centre of gravity of the beam is $3.5\text{ m}$ from $Q$ , find the reaction at $Q$ .

Worked solution (try it first)

$H = \dfrac{u^2\sin^2\theta}{2g}$
$= \dfrac{68^2\sin^2 42^\circ}{20}$
$\approx 103.5\text{ m}$ .

$T = \dfrac{2u\sin\theta}{g}$
$= \dfrac{136\sin42^\circ}{10}$
$\approx 9.1\text{ s}$ .

$R = \dfrac{u^2\sin2\theta}{g}$
$= \dfrac{4624\sin84^\circ}{10}$
$\approx 459.9\text{ m}$ .